Peaches Geldof, sometime journalist, wife and mother of two, died on Monday, aged 25; we don't know why, although that did not stop people calling it an overdose on Twitter and elsewhere. And why not? You can't libel the dead, or hurt them. It is a tragedy for her family, who already lost her mother, Paula Yates, in 2000, to an accidental heroin overdose; beyond that, nothing.

But silence is not admissible; this is death in the digital age, where social media respond in seconds and old media report for hours, and back and forth as events roll out with live reaction and speculation. These symbiotic beasts have only recently devoured Philip Seymour Hoffman, and Bob Crow. Bob Crow!

Because Geldof had an online "presence" and posted pictures of her children on Instagram, it was a death strangers felt they could participate in: virtual mourners, if you will, although computers can't weep. She was resurrected by a hashtag and her name. Is it the hashtag that is so offensive – inviting the idly curious and excitable to an online wake, perhaps to post the acronym "RIP" – its full wording presumably being too long-winded to hold attention? But at least it wasn't that heinous thing, an emoticon. Can we take solace in that?

Mere tributes, some say: it is touching, a reaching-out to a stranger now lost. But is it really? To me, it feels like entertainment posted on to a random face, a hand clutching blindly for something vivid. This is a moral dystopia where Katie Hopkins, who disagreed with Geldof on television recently about the best way to parent, was invited to grieve for her "arch nemesis" online, and was hounded for refusing to do so. Why should she? I do not agree with Hopkins about anything, but she is not a hypocrite. But you can forget that – Hopkins was invited to tweet an epilogue to the encounter, as if she were personally responsible, or a government department issuing a press release.

The grunt of synthetic emotion was gruesome. Geldof was prescient about her end, but not in the way that people think when reading such headlines as: "Peaches posted this picture with her tragic mum; hours later she was dead herself"; or worse, with the same illustration: "Together again". (I didn't know tabloids did eschatology.) She once told a newspaper: "Joe Bloggs who only earns 20 grand and really has to struggle doesn't want to see Brad and Angelina strolling round in their million-dollar mansions. He wants to see them falling apart because that will make him feel better about himself. It's deep in the mid-brain below the survival instinct. That lust to see a downfall. It's animalistic." How true; that is good journalism. After Twitter's defenestration, she led the News at Ten.

Television, where Geldof (and her mother) worked, murders genuine emotion; it is the parent of social media. The screenwriter Paddy Chayefsky, in his film Network (1976), foretold it all; he would have recognised Geldof instantly, seen her value. His characters, who worked in television, thought only in cliche and narrative arc (of which she had plenty because her mother is dead and her father is famous), scheming to produce "suicide of the week … execution of the week … the death hour!".

Everything is material to be monetised, and in the end they killed their leading man for ratings – what else is a network to do? And now comes Twitter, the parallel universe where one is expected to be present as a human in short bursts for as long as the lights stay on and people are awake. No wonder people were surprised when no drug paraphernalia or suicide note was found near Geldof's corpse: didn't she know her narrative, her lines?

Perhaps there is a connection between this sort of grief – which is not grief at all, but drama and distraction – and a growing deadness of spirit towards others. Geldof's father, who worked to give the desperate a face we could identify, must know that this is true; and that is bitter. Instead we have this – the late-capitalist digital death, a media event so intoxicating that even people who are not technically "celebrated" are seconded from their death scenes, to the benefit of nothing.

Deborah Orr: Many young mothers turn to their own mothers for support when they feel vulnerable. If heroin made Peaches feel connected to Paula Yates, its temptation would have been very complex and very great